Finite Group Databasebeta

Q32×Dic227 #44401593

order29056
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productQ32×Dic227

Splittings

SylowC227 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC22D8×D227
commutatorC8×C227C22×C4
FrattiniC2×C8C22×D227
FittingC2×Q32×C227C2
socle, prime radicalC22×C227C2×D8
cosocleC2×C8×C227C23
hypercenterC2×Q32D227
hypocenterC227C4×Q32
LCSG ▷ C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29056

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6369);